momentum-and-impulse-in-1d

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Exam code:9FM0

Impulse-momentum principle in 1D

Any object that has mass and is moving has momentum
Momentum measures the quantity of motion that an object has
The momentum of a particle is defined as the product of its mass ( $bold italic m$ kg) and its velocity ( $bold italic v bold space bold m bold space bold s to the power of bold minus bold 1 end exponent$ )
- Momentum = mv
The SI unit for momentum is $bold kg bold space bold m bold space bold s to the power of bold minus bold 1 end exponent$
Momentum is a vector quantity – so it has a magnitude and direction
- The direction of the momentum of a particle is the same as the direction of motion of the particle
- The momentum is negative if the velocity is negative

Impulse measures the effect of a force acting on a particle over time, it could be thought of as a “push”
If a constant force ( $bold italic F bold space bold N$ ) acts on a particle for $t$ seconds then the impulse ( $bold italic I$ ) of the force is defined to be the product of the force and time
- $bold italic I bold space bold equals bold space bold italic F bold italic t$
The SI unit for impulse is N s (newton seconds) which is equivalent to $bold kg bold space bold m bold space bold s to the power of bold minus bold 1 end exponent$
- This is the same as the units for momentum
Impulse is a vector quantity – so it has magnitude and direction
- The direction of the impulse of a force is the same as the direction of the force

The Impulse-Momentum Principle states that impulse is equal to the change in momentum
- <img alt=”bold italic I bold space bold equals bold space bold italic m bold italic v bold minus bold space bold italic m bold italic u” data-mathml='<math ><semantics><mstyle mathsize=”16px”><mi mathvariant=”bold-italic”>I</mi><mo mathvariant=”bold”> </mo><mo mathvariant=”bold”>=</mo><mo mathvariant=”bold”> </mo><mi mathvariant=”bold-italic”>m</mi><mi mathvariant=”bold-italic”>v</mi><mo mathvariant=”bold”>-</mo><mo mathvariant=”bold”> </mo><mi mathvariant=”bold-italic”>m</mi><mi mathvariant=”bold-italic”>u</mi></mstyle><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”19″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2219%22%20width%3D%2299%22%20wrs%3Abaseline%3D%2215%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmstyle%20mathsize%3D%2216px%22%3E%3Cmi%20mathvariant%3D%22bold-italic%22%3EI%3C%2Fmi%3E%3Cmo%20mathvariant%3D%22bold%22%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmo%20mathvariant%3D%22bold%22%3E%3D%3C%2Fmo%3E%3Cmo%20mathvariant%3D%22bold%22%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%20ma